A technician of the U. Geological Survey uses a mass spectrometer to determine the proportions of neodymium isotopes contained in a sample of igneous rock. Cloth wrappings from a mummified bull Samples taken from a pyramid in Dashur, Egypt. This date agrees with the age of the pyramid as estimated from historical records. Charcoal Sample, recovered from bed of ash near Crater Lake, Oregon, is from a tree burned in the violent eruption of Mount Mazama which created Crater Lake. This eruption blanketed several States with ash, providing geologists with an excellent time zone.

## Radiometric dating

Petrology Tulane University Prof. Stephen A. Nelson Radiometric Dating Prior to the best and most accepted age of the Earth was that proposed by Lord Kelvin based on the amount of time necessary for the Earth to cool to its present temperature from a completely liquid state. Although we now recognize lots of problems with that calculation, the age of 25 my was accepted by most physicists, but considered too short by most geologists.[rs_table_products tableName=”Best Dating Websites”]

Then, in , radioactivity was discovered. Recognition that radioactive decay of atoms occurs in the Earth was important in two respects: It provided another source of heat, not considered by Kelvin, which would mean that the cooling time would have to be much longer. It provided a means by which the age of the Earth could be determined independently.

Principles of Radiometric Dating. Radioactive decay is described in terms of the probability that a constituent particle of the nucleus of an atom will escape through the potential Energy barrier which bonds them to the nucleus. The energies involved are so large, and the nucleus is so small that physical conditions in the Earth i. T and P cannot affect the rate of decay.

The rate of decay or rate of change of the number N of particles is proportional to the number present at any time, i. So, we can write. After the passage of two half-lives only 0. This can only be done for 14 C, since we know N 0 from the atmospheric ratio, assumed to be constant through time. For other systems we have to proceed further. The only problem is that we only know the number of daughter atoms now present, and some of those may have been present prior to the start of our clock.

We can see how do deal with this if we take a particular case. The neutron emits an electron to become a proton. We still don’t know 87 Sr 0 , the amount of 87 Sr daughter element initially present. Thus, 86 Sr is a stable isotope, and the amount of 86 Sr does not change through time. So, applying this simplification,. The reason for this is that Rb has become distributed unequally through the Earth over time.

For example the amount of Rb in mantle rocks is generally low, i. Thus we could tell whether the rock was derived from the mantle or crust be determining its initial Sr isotopic ratio as we discussed previously in the section on igneous rocks. Two isotopes of Uranium and one isotope of Th are radioactive and decay to produce various isotopes of Pb. The decay schemes are as follows. Note that the present ratio of.

If these two independent dates are the same, we say they are concordant. We can also construct a Concordia diagram, which shows the values of Pb isotopes that would give concordant dates. The Concordia curve can be calculated by defining the following:. Zircon has a high hardness 7. Zircon can also survive metamorphism. Chemically, zircon usually contains high amounts of U and low amounts of Pb, so that large amounts of radiogenic Pb are produced.

Other minerals that also show these properties, but are less commonly used in radiometric dating are Apatite and sphene. Discordant dates will not fall on the Concordia curve. Sometimes, however, numerous discordant dates from the same rock will plot along a line representing a chord on the Concordia diagram. Such a chord is called a discordia. We can also define what are called Pb-Pb Isochrons by combining the two isochron equations 7 and 8.

Since we know that the , and assuming that the Pb and Pb dates are the same, then equation 11 is the equation for a family of lines that have a slope. The answer is about 6 billion years. This argument tells when the elements were formed that make up the Earth, but does not really give us the age of the Earth. It does, however, give a maximum age of the Earth. Is this the age of the Earth? Lunar rocks also lie on the Geochron, at least suggesting that the moon formed at the same time as meteorites.

Modern Oceanic Pb – i. Pb separated from continents and thus from average crust also plots on the Geochron, and thus suggests that the Earth formed at the same time as the meteorites and moon. Thus, our best estimate of the age of the Earth is 4. The initial ratio has particular importance for studying the chemical evolution of the Earth’s mantle and crust, as we discussed in the section on igneous rocks. Since K is one of the 10 most abundant elements in the Earth’s crust, the decay of 40 K is important in dating rocks.

But this scheme is not used because 40 Ca can be present as both radiogenic and non-radiogenic Ca. Since Ar is a noble gas, it can escape from a magma or liquid easily, and it is thus assumed that no 40 Ar is present initially. Note that this is not always true. If a magma cools quickly on the surface of the Earth, some of the Ar may be trapped. If this happens, then the date obtained will be older than the date at which the magma erupted. For example lavas dated by K-Ar that are historic in age, usually show 1 to 2 my old ages due to trapped Ar.

Such trapped Ar is not problematical when the age of the rock is in hundreds of millions of years. The dating equation used for K-Ar is: Some of the problems associated with K-Ar dating are Excess argon. This is only a problem when dating very young rocks or in dating whole rocks instead of mineral separates. Minerals should not contain any excess Ar because Ar should not enter the crystal structure of a mineral when it crystallizes.

Thus, it always better to date minerals that have high K contents, such as sanidine or biotite. If these are not present, Plagioclase or hornblende. If none of these are present, then the only alternative is to date whole rocks. Atmospheric Argon. Some 40 Ar could be absorbed onto the sample surface. This can be corrected for. Metamorphism or alteration. Most minerals will lose Ar on heating above o C – thus metamorphism can cause a loss of Ar or a partial loss of Ar which will reset the atomic clock.

If only partial loss of Ar occurs then the age determined will be in between the age of crystallization and the age of metamorphism. If complete loss of Ar occurs during metamorphism, then the date is that of the metamorphic event. The problem is that there is no way of knowing whether or not partial or complete loss of Ar has occurred. Examples of questions on this material that could be asked on an exam.

Radiometric Dating. Prior to the best and most accepted age of the Earth was that proposed by Lord Kelvin based on the amount of time necessary for the Earth to cool to its present temperature from a completely liquid state. Principles of Radiometric Dating Radioactive decay is described in terms of the probability that a constituent particle of the nucleus of an atom will escape through the potential Energy barrier which bonds them to the nucleus.

Thus, if we start out with 1 gram of the parent isotope, after the passage of 1 half-life there will be 0. Some examples of isotope systems used to date geologic materials. To see how we actually use this information to date rocks, consider the following: To account for this, we first note that there is an isotope of Sr, 86 Sr, that is: If we divide equation 4 through by the amount of 86 Sr, then we get: Note also that equation 5 has the form of a linear equation, i. How can we use this?

In nature, however, each mineral in the rock is likely to have a different amount of 87 Rb. Thus, once the rock has cooled to the point where diffusion of elements does not occur, the 87 Rb in each mineral will decay to 87 Sr, and each mineral will have a different 87 Rb and 87 Sr after passage of time. The Concordia curve can be calculated by defining the following: The discordia is often interpreted by extrapolating both ends to intersect the Concordia. Pb leakage is the most likely cause of discordant dates, since Pb will be occupying a site in the crystal that has suffered radiation damage as a result of U decay.

U would have been stable in the crystallographic site, but the site is now occupied by by Pb. An event like metamorphism could heat the crystal to the point where Pb will become mobile. Another possible scenario involves U leakage, again possibly as a result of a metamorphic event. U leakage would cause discordant points to plot above the cocordia. The Age of the Earth A minimum age of the Earth can be obtained from the oldest known rocks on the Earth. So far, the oldest rock found is a tonalitic Gneiss metamorphic rock rock from the Northwest Territories, Canada, with an age of 3.

This gives us only a minimum age of the Earth. Is it likely that we will find a rock formed on the Earth that will give us the true age of the Earth? From the Pb-Pb isochron equation 11 we can make some arguments about meteorites. First, it appears that meteorites have come from somewhere in the solar system, and thus may have been formed at the same time the solar system and thus the Earth formed.

## The discovery of the natural radioactive decay of uranium in of the various methods and techniques used to measure the age of Earth materials. . that are determined by dating appropriately selected igneous rocks. Radiometric dating, radioactive dating or radioisotope dating is a technique used to date materials such as rocks or carbon, in which trace radioactive . The age that can be calculated by radiometric dating is thus the time at which the rock or . This scheme is used to date old igneous and metamorphic rocks, and has also .

Beta Decay: By , it was found to be 1. In , science firmly established that the earth was 3. The study of geology grew out of field studies associated with mining and engineering during the sixteenth to nineteenth centuries.

Petrology Tulane University Prof. Stephen A.

Geologists use radiometric dating to estimate how long ago rocks formed, and to infer the ages of fossils contained within those rocks. Radioactive elements decay The universe is full of naturally occurring radioactive elements.

## 8.4 Isotopic Dating Methods

Radiometric dating , radioactive dating or radioisotope dating is a technique used to date materials such as rocks or carbon , in which trace radioactive impurities were selectively incorporated when they were formed. The method compares the abundance of a naturally occurring radioactive isotope within the material to the abundance of its decay products, which form at a known constant rate of decay. Together with stratigraphic principles , radiometric dating methods are used in geochronology to establish the geologic time scale. By allowing the establishment of geological timescales, it provides a significant source of information about the ages of fossils and the deduced rates of evolutionary change. Radiometric dating is also used to date archaeological materials, including ancient artifacts. Different methods of radiometric dating vary in the timescale over which they are accurate and the materials to which they can be applied.

## Radiometric Dating

Originally fossils only provided us with relative ages because, although early paleontologists understood biological succession, they did not know the absolute ages of the different organisms. It was only in the early part of the 20th century, when isotopic dating methods were first applied, that it became possible to discover the absolute ages of the rocks containing fossils. In most cases, we cannot use isotopic techniques to directly date fossils or the sedimentary rocks they are found in, but we can constrain their ages by dating igneous rocks that cut across sedimentary rocks, or volcanic ash layers that lie within sedimentary layers. Isotopic dating of rocks, or the minerals in them, is based on the fact that we know the decay rates of certain unstable isotopes of elements and that these rates have been constant over geological time. One of the isotope pairs widely used in geology is the decay of 40 K to 40 Ar potassium to argon It has a half-life of 1. In order to use the K-Ar dating technique, we need to have an igneous or metamorphic rock that includes a potassium-bearing mineral. One good example is granite, which normally has some potassium feldspar Figure 8. Feldspar does not have any argon in it when it forms. Over time, the 40 K in the feldspar decays to 40 Ar.

Лунный свет проникал в комнату сквозь приоткрытые жалюзи, отражаясь от столешницы с затейливой поверхностью.

Он быстро подошел к ним и остановился в нескольких сантиметрах от дрожащего Чатрукьяна. – Вы что-то сказали. – Сэр, – задыхаясь проговорил Чатрукьян. – ТРАНСТЕКСТ вышел из строя.

## Radiometric Dating Methods

Беккер перешел на ломаный английский: – Спасибо. Не могли бы вы мне помочь. – О да, конечно, – медленно проговорила женщина, готовая прийти на помощь потенциальному клиенту. – Вам нужна сопровождающая. – Да-да. Сегодня мой брат Клаус нанял девушку, очень красивую. С рыжими волосами. Я тоже хочу. На завтрашний день, пожалуйста. – Ваш брат Клаус приходил к нам? – Женщина вдруг оживилась, словно говорила со старым знакомым.

– Да. Он очень толстый.

Сьюзан была понятна боль, которую испытывал шеф. Его так просто обвели вокруг пальца. Танкадо не собирался продавать свой алгоритм никакой компьютерной компании, потому что никакого алгоритма не. Цифровая крепость оказалась фарсом, наживкой для Агентства национальной безопасности. Когда Стратмор предпринимал какой-либо шаг, Танкадо стоял за сценой, дергая за веревочки.

Ты вскрыла мою электронную почту. – А ты отключил моего Следопыта. Хейл почувствовал, как кровь ударила ему в голову. Он был уверен, что спрятал все следы, и не имел ни малейшего понятия о том, что Сьюзан были известны его действия. Понятно, почему она не хотела верить ни одному его слову. Он почувствовал, как вокруг него выросла стена, и понял, что ему не удастся выпутаться из этой ситуации, по крайней мере своевременно.

И он в отчаянии прошептал ей на ухо: – Сьюзан… Стратмор убил Чатрукьяна.

Там проблема с электричеством. – Я не электрик. Позвони в технический отдел. – В куполе нет света. – У тебя галлюцинации. Тебе пора отправляться домой.

Немец не ожидал такого оборота. – Wasmachst… – Помолчите! – Беккер перешел на английский. – У вас в номере проститутка? – Он оглядел комнату. Роскошная обстановка, как в лучших отелях. Розы, шампанское, широченная кровать с балдахином.

Стратмор скачал файл с Цифровой крепостью и запустил его в ТРАНСТЕКСТ, но программа Сквозь строй отказалась его допустить, потому что файл содержал опасную линейную мутацию. В обычных обстоятельствах это насторожило бы Стратмора, но ведь он прочитал электронную почту Танкадо, а там говорилось, что весь трюк и заключался в линейной мутации. Решив, что никакой опасности нет, Стратмор запустил файл, минуя фильтры программы Сквозь строй.

Сьюзан едва могла говорить. – Никакой Цифровой крепости не существует, – еле слышно пробормотала она под завывание сирены и, обессилев, склонилась над своим компьютером. Танкадо использовал наживку для дурачков… и АНБ ее проглотило.

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